Edexcel S2 2015 June — Question 1 11 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2015
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPoisson distribution
TypeSingle period normal approximation - large lambda direct
DifficultyModerate -0.3 This is a straightforward application of Poisson distribution with standard parts: (a) direct Poisson probability calculation, (b) scaling the rate parameter, and (c) normal approximation for large λ. All three parts follow textbook procedures with no conceptual challenges or novel problem-solving required, making it slightly easier than average.
Spec2.04d Normal approximation to binomial

In a survey it is found that barn owls occur randomly at a rate of 9 per 1000 km\(^2\).
  1. Find the probability that in a randomly selected area of 1000 km\(^2\) there are at least 10 barn owls. [2]
  2. Find the probability that in a randomly selected area of 200 km\(^2\) there are exactly 2 barn owls. [3]
  3. Using a suitable approximation, find the probability that in a randomly selected area of 50000 km\(^2\) there are at least 470 barn owls. [6]

In a survey it is found that barn owls occur randomly at a rate of 9 per 1000 km$^2$.

\begin{enumerate}[label=(\alph*)]
\item Find the probability that in a randomly selected area of 1000 km$^2$ there are at least 10 barn owls. [2]

\item Find the probability that in a randomly selected area of 200 km$^2$ there are exactly 2 barn owls. [3]

\item Using a suitable approximation, find the probability that in a randomly selected area of 50000 km$^2$ there are at least 470 barn owls. [6]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S2 2015 Q1 [11]}}